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Ramanujan enforced. (Posted on 2010-08-02) Difficulty: 4 of 5
1,729 is the least integer which equals the sum of two positive cubes in two different ways (see "taxicab number" on the web):
1,729 = 12^3+1^3 and 1,729 = 10^3+9^3.

a) Find an integer which equals the sum of two positive cubes in THREE different ways.
There is more than one solution.

b) Erasing the word "positive" in the 1st statement allows a lesser positive integer(s??) number(s??) to be presented as a sum of two cubes in two different ways.
Find it (them??).

  Submitted by Ady TZIDON    
Rating: 4.0000 (1 votes)
Solution: (Hide)
a. Smallest example:
167^3 + 436^3 = 87539319
228^3 + 423^3 = 87539319
255^3 + 414^3 = 87539319

For additional examples and inclusion of negative integers see Charlie's solution

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Puzzle ThoughtsK Sengupta2024-06-18 10:33:45
re(2): computer solutionJustin2010-08-02 16:34:03
SolutionsolutionsDej Mar2010-08-02 16:16:37
re: computer solutionCharlie2010-08-02 16:08:54
Solutioncomputer solutionCharlie2010-08-02 16:03:48
computer solutionJustin2010-08-02 15:18:11
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